Even countries with universal health care have private hospitals, they'll take your money. One near me asks you to consider paying for their services out of your retirement funds if you don't have private health insurance.
There are plenty of people who cannot get care at government hospitals in countries with "universal healthcare", because of waiting lists, because the government doesn't consider the treatment they need to be worthwhile, etc. You could easily find some of those people on crowdfunding sites, and the media occasionally writes about such cases. The problem is that paying for their treatment at a private hospital would be very expensive, unless the ransomware would accept a partial crowdfunding contribution.
In Sweden, where my opinion of the public health care is that it's useless (unless you're having a really acute problem), I've looked for private hospitals to get help from. No such luck! Finding a specialist to help you, no matter if you have money and are willing to pay feels close to impossible, at least for the things that I've needed help with.
I've never understood why dental care isn't included when you otherwise have universal healthcare. Why single out dental problems? It's about as impossible to just ignore having an infected tooth that needs to be pulled out as it is not doing anything about a broken arm.